Weak limit of homeomorphisms in \(W^{1,n-1}\): invertibility and lower semicontinuity of energy

Weak limit of homeomorphisms in \(W^{1,n-1}\): invertibility and lower semicontinuity of energy

Let \(\Omega\), \(\Omega'\subset\mathbb{R}^n\) be bounded domains and let \(f_m\colon\Omega\to\Omega'\) be a sequence of homeomorphisms with positive Jacobians \(J_{f_m} >0\) a.e. and prescribed Dirichlet boundary data. Let all \(f_m\) satisfy the Lusin (N) condition and \(\sup_m \int_{...

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Veröffentlicht in:arXiv.org 2023-09
Hauptverfasser: Doležalová, Anna, Hencl, Stanislav, Molchanova, Anastasia
Format: Artikel
Sprache:eng
Schlagworte:
Dirichlet problem
Jacobians
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Zusammenfassung:Let \(\Omega\), \(\Omega'\subset\mathbb{R}^n\) be bounded domains and let \(f_m\colon\Omega\to\Omega'\) be a sequence of homeomorphisms with positive Jacobians \(J_{f_m} >0\) a.e. and prescribed Dirichlet boundary data. Let all \(f_m\) satisfy the Lusin (N) condition and \(\sup_m \int_{\Omega}(|Df_m|^{n-1}+A(|\text{cof} Df_m|)+\phi(J_f))
ISSN:2331-8422